Bradley Davies, Casey Laulala and Tom James all picked injuries in the defeat to Newport Gwent Dragons, while Gethin Jenkins is still struggling to return following toe surgery.
They join Leigh Halfpenny, Ben Blair and Richard Mustoe on the injury list, while Tom Shanklin was recently forced into retirement.
"We are really down to our bare minimum behind," said Young.
"Training is a little bit complicated at the moment, as we are not sure if Tom (James) or Casey are going to be available.
"At this stage of the season, a lot of players are going to be carrying bumps and bruises. There are very few who aren't. We are no different to anyone else in that respect.
"One thing I will confirm is that Jamie Roberts definitely will be playing. It could be 12, it could be 13, it could be wing, it could be full-back.
"It would be nice to go down to Llanelli with a full team, but if you don't you just roll your sleeves up and get on with it.
"I'm certainly not going to offer that as an excuse. I still think we have enough quality in our team to go out and get a result."
The 22-times capped lock Davies suffered a chest injury during last Friday's defeat to the Newport Gwent Dragons and is a major concern ahead of Wales' clash with the Barbarians on June 4.
Davies could be ruled out for up to six weeks, meaning he's also likely to miss the Magners League play-offs, if the Blues finish in the top four.
But the Blues are confident that Davies will recover to full fitness well in advance of the World Cup.
"He has had a scan," added Blues director of rugby Dai Young.
"It doesn't need an operation or anything, but he certainly needs a number of weeks off. "It's an impact injury to his chest, so the first week or so will determine how long it's going to be.
"You are probably looking at anything between two to six weeks. Who knows about his availability for the Baa-Baas game?
"There's certainly no problems with the World Cup."
The capital city side will again be without Jenkins and he is also a doubt for the Baa-Baas clash. The British & Irish prop has not played since the toe operation he underwent in January.
"He's desperate to play," added Young.
"He wanted to be a part of it last week against the Dragons, even to the point of taking the water on for the boys. He's hugely frustrated that he's not a part of it at the minute.
"He's running, but the issue is actually putting a lot of force through it in the scrum. Your foot has got to take a lot of pressure there.
"If he was playing in a different position, he would probably be okay, but you've got a lot of pressure coming against you and behind you in the scrum."
But Jenkins could feature if the Blues reach the play-offs. They currently lie fourth in the league and need to beat the Scarlets to remain fourth.
"If we did get to the play-off final at the end of this month, Gethin might be available for that," added Young.
"He wouldn't be far off. He's not far from there. But we are very conscious of not pushing him out there too early which could push him back.
"There's a big picture to look at as well, isn't there?"
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